anytime power isn't a variable( takeoffs and landings if you set it and forget it ) pitch is airspeed and power is altitude. Now when power is variable ( cruise flight ) power then is airspeed and pitch is altitude.
Wouldn't it be interesting if the laws of physics just reversed themselves when an engine turned on or off? But, as you might suspect, they don't.
First, you'll never make heads or tails out of this discussion by using the word "pitch". Get rid of it for the time being. Pitch is the angle that the longitudinal axis makes with the horizon and it is equal to the sum of the angle of attack (AoA) and climb angle. Pitch never controls anything; it's a result, not a cause. The real word(s) you should be using is "angle of attack". AoA controls airspeed in any steady flight. Other than brief fluctuations, to change your airspeed, you need to change your AoA. This is true regardless of whether you have power or not.
Where the confusion comes in is in level flight when you wish to make an airspeed change. For instance, to go faster, you normally add power and then increase the pressure on the yoke to maintain altitude. Since you make both control movements at the same time, the cause/effect connection is a little obscure. The actual speed increase comes from pushing forward on the yoke; if you didn't add power, you would find yourself in a descent. If you only added power, you'd find yourself in a climb at about the same airspeed, maybe slower.
Altitude control is determined by the quantity of excess power (or thrust). An aircraft without power will descend, because maintaining level flight requires power. If you have excess power beyond what is needed for level flight, the airplane will climb. If you have a power deficit, the aircraft will descend. You can change the quantity of excess power in two ways:
- Change the throttle setting, or
- Change the drag on the airplane by changing your airspeed.
For instance, if you're in cruise, if you pull back on the yoke, you will slow the airplane, which reduces the drag on the airplane which will cause the airplane to climb. Unless, of course, you get behind the power/drag curve and then pulling back on the yoke will cause the airplane to descend.
This is the way the physics works, so you don't need to come up with different sets of rules of for power/no power, or front-side/backside of the power curves.